OK, those small differences sound like they could be rounding errors. Agreed, it shouldn't happen. I'll do some tests here later to see if I can reproduce. Is the master PSD file 16 or 8 bit color depth?
That said, I have to make some general remarks here, because I'm a little concerned about your procedures. They can potentially cause problems.
Assigning profiles won't do any good if it's not right to begin with, or if the file is untagged (doesn't have a profile). That will only make it worse. What you need to do is keep track of the embedded profile from the start. You do that here:
If the profile isn't what you want, you convert, not assign. The working space is not important. The embedded profile, whatever it is, will always override the working space.
Also, I'm very skeptical to the current trend in the Mac community to use Display P3 everywhere. If you're also using the same Display P3 as monitor profile, which is what it's intended for, you're actually disabling and turning off all display color management. The thing is, if the source and destination profiles are identical, that's a "null transform". It's all cancelled out. Nothing is converted, no change at all, which is the definition of no color management.
At this point, it doesn't even matter what the profile is. It could be anything - as long as they're the same, there is no color management. Display P3 to Display P3 behaves exactly the same way as ProPhoto to ProPhoto, or sRGB to sRGB.
Now you probably begin to see the danger. This will all look perfectly fine as long as you're inside the Apple bubble, with fellow Apple users. But move outside it, and all kinds of things can happen, because you've all been working without color management. You can drop embedding the profile, and no Mac user will notice it. But others will!
Display P3 is a monitor profile. Generic, but very widely used instead of a calibrator. It wasn't intended as a standard RGB profile, but that's how it's used now.
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